Please help me to prove.

Prove that if domain conformaly maps to unit disc then it's simply connected domain.

Thanks!

Printable View

- November 19th 2011, 07:03 AMsinichkoComplex Analysis - simply connected domain
Please help me to prove.

Prove that if domain conformaly maps to unit disc then it's simply connected domain.

Thanks! - November 19th 2011, 08:42 AMOpalgRe: Complex Analysis - simply connected domain
You need to assume that the conformal map is bijective (and therefore invertible), otherwise the result is not true.

Suppose that S is a loop in . The image f(S) of S is a loop in the simply-connected space D. So there is a continuous transformation in D that contracts this loop to a point. The image in of that deformation under the map will be a continuous transformation in which contracts S to a point S to a point. - November 22nd 2011, 12:54 PMsinichkoRe: Complex Analysis - simply connected domain
[QUOTE=Opalg;696240]You need to assume that the conformal map is bijective (and therefore invertible), otherwise the result is not true.

Thanks a lot!